To be clear, you have not tried a new yellow cartridge yet, correct?
This issue could be one of two things. either A, you need a new yellow cartridge.
Or B, the printhead is damaged or dirty and needs to be cleaned by hand, or replaced.
Specifically the contacts inside the printhead that read your yellow cartridge.. It should be small electrical contacts, and those contacts need to be gently cleaned.
If you try a new cartridge and it cant read it, and you try to clean the contacts and it still cannot read it. Then you may need to replace the printhead. However, It would help if I knew the exact model number of the photosmart printer you have, so I can provide model specific info about the printhead and how to clean it.
But we definitely want to try a new yellow cartridge itself.
Please respond when you can and we will continue~
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Senior Technician and Network Switching Systems Operator / Maintainer.